The Englishman is out of contract at the Emirates at the end of the season, and is reportedly in discussions over a new contract at the moment, however there are said to be complications with the negotiations.
Due to Wilshere's track record of injuries, the Gunners are understood to be looking to reduce the midfielders salary, with an opportunity of gaining some bonuses through appearances and achievements.
With negotiations currently at a stand still with the Gunners, Liverpool are reportedly ready to offer the Englishman £90,000 a week - his current salary at Arsenal.
German midfielder Emre Can is expected to leave the Merseyside giants in the summer, with the former Bayer Leverkusen man in the final months of his contract at Anfield.
Despite the potential departure of Can, Liverpool have already replaced the German international with RB Leipzig midfielder Nabi Keita, and therefore a deal for Wilshere seems very unlikely.
With both Keita and Jordan Henderson able to play in the middle of the park it does seem somewhat ridiculous to suggest that Jürgen Klopp would be on the hunt for a new midfielder.